Gravity waves are an important part of the momentum budget of the atmosphere. Despite this, parameterizations of gravity wave spectra in atmospheric models are poorly constrained. Gravity waves are formed by jet streams, flow over topography, and convection, all of which produce pressure perturbations as they propagate over the Earth's surface, detectable by microbarometer arrays used for sensing infrasound. In this study, observations of gravity waves between 2007 and 2011 at an infrasound station in the Ivory Coast, West Africa, are combined with meteorological data to calculate parameters such as intrinsic phase speed and wavenumber. Through spectral analysis, the seasonal and daily variations in all gravity wave parameters are examined. The gravity wave back azimuth varies with the migration of the Intertropical Convergence Zone, a region of intense convection, supporting previous studies. Daily variations in gravity wave arrivals at the station can be linked to two distinct convective cycles over the land and ocean. This was achieved by combining the gravity wave parameters with lightning strikes detected by the Met Office's Arrival Time Difference lightning detection system. Noise generated by turbulence in the middle of the day was found to attenuate smaller pressure amplitude gravity waves, artificially amplifying the daily variations in some gravity wave parameters. Detection of daily and seasonal variations in gravity wave parameters has the potential be used to improve the representation of gravity wave spectra in atmospheric models.
- Variations in gravity wave activity at a tropical infrasound station are linked with daily and seasonal local and remote convective cycles
- Gravity wave travel distance affects the wavelength, speed, and amplitude of gravity waves
- Gravity waves took on average 6 hr to propagate from a thunderstorm source to microbarometer array
Convection, topography, and jet streams cause atmospheric disturbances that lead to the generation of atmospheric gravity waves (GWs) (Fritts & Alexander, 2003). GWs are important as they transport momentum through the atmosphere, which affects the stratospheric circulation (Beres et al., 2004), and they generate turbulence as they break (Knox et al., 2008). Despite their importance, parameterizations for GWs are ill constrained in models, and more observations are needed to improve them (Beres et al., 2004; Lott & Guez, 2013 and Richter et al., 2010). In their review, Geller et al. (2013) demonstrate that there are few observation methods for GW detection that have extensive temporal and global coverage. Most existing observations originate from satellite measurements which observe GWs in the stratosphere (de Groot-Hedlin et al., 2017). At the surface, GWs produce perturbations in surface pressure which can be observed using sensitive barometers. Time series of microbarometer data have been used previously to infer GW properties at the surface (Aplin & Harrison, 2003; Balachandran, 1980; le Pichon et al., 2002; Marlton et al., 2019).
The direction and velocity of wave propagation can be derived using arrays of three or more instruments (Blanc et al., 2014; Farges et al., 2003; le Pichon et al., 2002). Larger arrays of barometers such as those used in the USArray network have been used to detect convectively generated GWs at the surface with time periods of 2–6 hr (Balachandran, 1980; de Groot-Hedlin et al., 2017; Jacques et al., 2015). However, the microbarometer network used in de Groot-Hedlin et al. (2017) only covers parts of the mainland United States. In contrast, the Comprehensive Nuclear-Test-Ban-Treaty Organization's International Monitoring System (IMS) will consist of 60 microbarometer arrays, also referred to as infrasound stations (IS), across the globe (Christie & Campus, 2010), used as a verification technique for atmospheric nuclear tests (Dahlman et al., 2009). Currently, 49 arrays have been installed and certified, providing data in real time to the International Data Center in Vienna (status in June 2018). Infrasound microbarometers measure small pressure fluctuations on the order of millipascals up to tens of pascals with a flat response over the frequency band from 0.08 to 4 Hz sampled at 20 Hz (Ponceau & Bosca, 2010). GWs have frequencies much lower than 0.08 Hz and generate pressure perturbations several orders larger than that of infrasound. This, combined with the flat response range, results in a reduction in pressure amplitude at lower frequencies. A transfer function is therefore applied to the infrasound data to correct for the response as a function of frequency. Each infrasound array consists of at least four microbarometers with an array aperture of approximately 1 km, which provides a global network, capable of detecting and characterizing GWs as demonstrated in Marty et al. (2010). Some IMS stations have been operational for over a decade allowing local GW climatologies to be created. Blanc et al. (2014) undertook an analysis of 10 years of GW observations from IS 17 (IS17), located in the Ivory Coast, Western Africa, and found seasonal variations in the GW back azimuth due to a seasonal shift in the Intertropical Convergence Zone (ITCZ), as inferred by a satellite-borne Lightning Imaging Sensor. The ITCZ is a zone of low pressure that forms at the convergence of the north and south trade winds, causing convection. It shifts northward in the Northern Hemisphere summer and southward in the Northern Hemisphere winter, due to radiative heating (Wallace & Hobbs, 2006). Convective systems in this region form from approximately 1 km and can extend up approximately 12 km (Stein et al., 2015).
In this study, the analysis in Blanc et al. (2014) is extended by combining the GW measurements with meteorological observations to calculate wavenumbers and velocity perturbations as shown in Marlton et al. (2019) and summarized in section 2. The aim of this is to allow the easier use of GW data from infrasound networks for meteorological applications. In the remainder of this study lightning strike location data from the Met Office's Arrival Time Difference network (ATDnet) lightning system is used to link the observed GW time series at IS17 to daily and seasonal variations in local thunderstorm activity.
2 Deriving GW Parameters From the Ivory Coast IS
IS17 is a four-element infrasound array located in the Ivory Coast, West Africa, 6.67 N, 4.89 W, approximately 180 km inland from the east Atlantic Ocean. The four microbarometers are arranged in a triangular configuration with the fourth instrument at the center, with a distance between each microbarometer of approximately 1 km. As a GW passes over the array it induces pressure perturbations, delayed sequentially at each microbarometer. A GW's back azimuth ϕ, pressure perturbation p′, ground-based phase velocity c, and frequency ω can be derived from differences between the individual sensor time series. Two methods can be implemented to achieve this. First, a Progressive Multi-Channel Correlation (PMCC) algorithm originally described in Cansi (1995) and adapted by le Pichon et al. (2002) and Farges et al. (2003) is suitable for use on infrasonic waves and GWs. Second, a Fisher statistical test can be used to see if the multiple time-shifted pressure time series are correlated (Evers, 2008) in the time domain (Melton & Bailey, 1957) or frequency domain (Smart & Flinn, 1971). For this analysis, GWs detected at IS17 using the PMCC method are used with the following assumption: the waves are linear plane waves with no curvature as they are distant from their source. The PMCC analysis implemented here scanned the pressure time series for GWs with periodicities from 10 to 165 min.
Lindzen and Tung (1976), Balachandran (1980), and Chimonas and Hines (1986) showed that GWs detected near the surface and for long periods are likely to be ducted waves. Figure 1 shows averaged profiles of the u and v wind components and Brunt-Vaisala frequency N, squared over IS17 from the European Centre for Medium-Range Weather Forecasting high-resolution model. A low-level jet peaks at 4 km, and N makes a step change at this height indicating the presence of temperature and wind ducting mechanisms up to a height of approximately 4 km (Chimona and Hines 1986, Crook, 1988, and Nappo, 2013). Furthermore, the GWs detected in Blanc et al. (2014) are detected 100 km away from the convective source, indicating a ducting mechanism is present stopping the GWs propagating away into the upper atmosphere.
The values , and u′ were calculated from the IS17 GW bulletin for the years between 2007 and 2011 and are analyzed in sections 4 and 5. There is good data availability over this period. However, there is a gap in observations in February 2008.
3 Lightning Observations as a Proxy for Convection Over IS17
To explore the relationship between convective systems and the GWs observed at IS17, a method of inferring the time and location of the convection is needed. Convective systems can be observed using weather radar, daily precipitation measurements, or by examining lightning strike data. Daily precipitation measurements and weather radar observations are limited over Africa, which moves the emphasis in observing convection in this region to remote sensing methods. For example, the Tropical Applications of Meteorology use SATellite and ground-based observations (Maidment et al., 2014), and Tropical Rainfall Measurement Mission (TRMM; Kummerow et al., 1998) use satellite-based measurements to infer rainfall estimates. However, rainfall does not always imply convection so this method has limitations in inferring convection. The TRMM satellite was also equipped with a Lightning Imaging Sensor; however, the scanning pattern for this sensor limits the temporal and spatial sampling resolution. An alternative to measuring lightning strikes from orbit is to use a terrestrial radio detection system, such as a very low frequency radio time arrival differencing system. Lightning strikes produce a broadband electromagnetic wave (or sferic) which can be detected by a radio antenna thousands of kilometers from the lightning strike. By having multiple antennas spaced across the globe, the position of each lightning strike can be inferred by examining the arrival time of the same sferic at each antenna. The UK Met Office's ATDnet allows lightning detection over Europe, the Atlantic, and much of Africa (Nash et al., 2006). ATDnet records lightning strikes as they occur with an accuracy of ±50 km giving excellent temporal and spatial resolution. A significant limitation on this approach is that lightning serves only as a proxy for convection; nonelectrically active convection may also occur which does not yield detectable lightning.
ATDnet data for lightning strikes were bounded by the geographical region bounded by 10°S to 20°N and 20°W to 10°E, an area centered on IS17, for the years 2007 to 2011. This period was chosen to match GW bulletins availability. Composite two-dimensional histograms with 0.25° resolution were created from the subset of lightning data for each month of the year. Figure 3 shows 2-D histograms for the months of January April, July, and October using data from the ATDnet system. The ITCZ is apparent as a strip of thunderstorms which shifts to the north in the summer and south in Northern Hemispheric winter. To understand further how the position and distance of the thunderstorms change with the GW parameters, the polar coordinates of each lightning strike relative to IS17 are calculated and are retained for further analysis.
4 Seasonal and Daily Analysis of GW Parameters at IS17
The analysis methodology given in section 2 was applied to the IS17 GW bulletins between 2007 and 2011. The study period here is a smaller subset of that shown in Blanc et al. (2014) which spanned 10 years. This is because both meteorological data and GW detections are only available between 2007 and 2011.
Figures 4 and 5 show boxplots of each derived parameter binned by 30-day periods to highlight the seasonal variations. Figure 4a reproduces the annual variation in ϕ shown in Blanc et al. (2014), and there are also clear annual variations in p′ and u′ in Figures 4c and 5b, respectively. There is evidence to suggest biannual variation in parameters , , and kH in Figures 4b, 4d, and 5a, respectively. This is likely due to the ITCZ passing over IS17 twice a year. Lightning strike distance is plotted in Figure 5d; this was calculated by selecting lightning strikes that had a bearing which fell within the interquartile range of the GW ϕ for each 30-day period. It also exhibits annual variation, where the median distance peaks at an average of 1,300 km in December and January when the ITCZ, shown in Figure 3a, is more distant. The median distance is at a minimum when the ITCZ passes from north to south in September. Figure 5c shows there are about 300 GWs detected a month, which equates to 10 GWs passing over the station daily, in agreement with Blanc et al. (2014).
To further explore the periodicities in each GW parameter, a Lomb periodogram (Lomb, 1976) is created. The Lomb periodogram method is chosen as it can calculate the periodicities from irregularly sampled time series, as is the case for the GW detection times. Due to the ~104 observations, the fast Lomb routine shown in Press et al. (2007) is implemented.
Figure 6 shows Lomb periodograms for GW parameters detected at IS17 during the study period. All parameters except kH show an annual periodicity, with all parameters also showing a 6-month periodicity, which further supports the hypothesis that GW parameters are being modulated by the seasonal variations in ITCZ's position, which passes over IS17 twice a year. Furthermore, there are also daily periodicities shown for all GW parameters in Figure 6, these will be further investigated in section 5. To extract the annual and biannual periodicities found in Figures 4 and 5 more effectively, annual composites have been computed for each GW parameter, which are shown in Figure 7.
Figure 7a shows the annual variation in ϕ which shifts from a southerly direction in December to an easterly direction during April to June. The stalling during this period is likely due to the preonset stages of the West African Monsoon, which causes the ITCZ to stall at 5°N, IS 17's latitude, in May and June (Sultan & Janicot, 2003), before reaching full intensity and moving north in August. GW ϕ continues to shift to a northerly direction during July and August before backing back to an easterly direction in September. This is due to the ITCZ shifting southward, heading into southern hemispheric summer. This agrees with the findings in Blanc et al. (2014). Although convection and GW generation occur in a broad band on either side of IS17 due to the ITCZ, the majority of GWs observed here have a component from an easterly direction. This is because winds over IS17 are predominantly from an easterly direction (Hart, 1977) causing the propagation of GWs in a westward direction. Figure 1 shows the annual mean horizontal wind profile over IS17; centered at 4 km in altitude is an easterly jet which forms part of the ducting mechanism (Lindzen & Tung, 1976; Nappo, 2013) for the GWs observed here as suggested in section 2.
Figure 7b shows the annual variation in . During December, January, and August, is larger than during the equinox months, indicating that when the ITCZ is more distant the of observed GWs is higher. Given that the GWs have propagated further to reach IS17, there is likely to be more GW attenuation along the path. Attenuation occurs due to interactions in the background flow, such as turbulent dissipation or wave-wave interactions (Fritts & Alexander, 2003). Figure 7g shows that GW detections are lowest in January–February and August when the ITCZ is most distant, implying GW attenuation. As well as attenuation the top of the GW duct is unlikely a perfect reflector, and some of GW energy may pass through and propagate into the upper atmosphere. Second, Gill (1982) states that slower waves have shorter wavelengths (larger kH) than faster waves with longer wavelengths (small kH); this is also shown in Figure 7e where kH is smaller when the ITCZ is more distant, and this is also reflected in shown in Figure 7d. Thus, for more distant thunderstorm sources, faster GWs are observed.
Figure 7c shows the annual variation of the pressure amplitude of the wave p′. When the ITCZ is overhead p′ is larger, indicating that as the GW travel further their p′ decreases, meaning the amplitude of the wave becomes smaller for more distance wave sources. The horizontal velocity perturbation u′ also follows this trend. de Groot-Hedlin et al. (2017) state that in their studies slower GW were associated with larger p′. Combining this with the fact that shorter wavelength waves are more strongly attenuated, this explains the decrease in p′ with propagation distance. As well as distance from the IS station, further consideration should be given to how the convective intensity may affect the GW parameters. Beres et al. (2004) showed that GW spectra vary with the convective source. Figure 3 shows that convective intensity is weakest in December and January. Average monthly lightning counts, used here as a proxy for convective intensity, are plotted alongside monthly averages of GW parameters and are shown in supporting information Figure S1. Decreases in p′ and increases in in December–January could have contributions from reduced convective activity in addition to the long distance the GWs have to propagate. However, it is hard to isolate the effects on intensity from the more prominent signal from propagation distance.
In summary, as the ITCZ becomes more distant from IS17 we see a reduction in the amount of GWs and that the GWs that are detected tend to have longer wavelengths, lower and kH, and larger which is likely due to attenuation of GWs with smaller . As the shorter GWs are not present this also causes a decrease in the size of p′ and u′ with distance from the ITCZ in the background flow. Here an explanation for the seasonal variation in GW parameters has been discussed. In the next section, the daily variations in GW activity are explored.
5 Daily Variations
It has been established that the position and distance of thunderstorms in the ITCZ relative to IS17 modulate the properties of GWs observed on seasonal time scales; it was also shown in Figure 6 that a daily periodicity is present in the derived GW parameters. It is likely that aspects of the convective diurnal cycle are being observed within the GW parameters.
Before examining the daily variation in GW parameters, it is important to understand the local convective cycle first. Figure 8 shows 2-D histograms of lightning strikes by hour of day for April between 2007 and 2011. It can be seen between 3 and 12 UT (Figures 8b–8e) that most thunderstorms occur over the ocean. Between 15 and 0 UT (Figures 8a–8f) most thunderstorms occur over the land, implying two distinct convective cycles which could be the source of the daily variation seen in Figure 4. Figures S2 and S3 show 2-D histograms of lightning strikes between 2007 and 2011 for July and December, respectively. Figure 9 shows total lightning strikes plotted by hour of the day for the months April, July, and December for the subset area described in section 3. Also plotted are the total lightning strikes over land and over ocean. It can be seen in all three plots that the lightning strike intensity over the oceans peaks between 6 and 9 UT, whereas lightning activity over land peaks between 14 and 21 UT. The relative contribution from the two convective regimes varies throughout the year, and this is due to the position of the ITCZ; in December when the ITCZ is due south the ocean convective regime is dominant and in July the continental convective scheme is dominant when the ITCZ is due north.
Figure 10 shows the daily variation in the median and interquartile range of GW parameters for April, July, and December. It should be noted that no data was available for the hours of 23 to 0 UT due to the processing method utilized which exhibits a wraparound issue around midnight. With the exception of ϕ all GW parameters follow a similar pattern in daily variation throughout the year; the magnitude does however change, for example, in Figures 10c and 10f the p′ and u′ quantities are largest when the ITCZ is closest in April. Figure 10a shows ϕ; for April (blue), between 18 and 6 UT there are GWs with ϕ propagating from the NE indicating they are from thunderstorms generated over land, and between 6 and 17 UT, ϕ shifts to the SE, indicative of GWs propagating from ocean and coastal areas. Figure 9a shows that peak thunderstorm activity over the ocean occurs between 03 and 12 UT, and peak thunderstorm activity occurs over land between 15 and 0 UT. This lag of approximately 6 hr is due to the distance GWs have to travel, which is also outlined in Figure 5. Back azimuth, ϕ for July (green) is from a NE direction between 20 and 9 UT; between 9 and 19 UT the ϕ begins to shift to a more east direction with increased variability indicating there may be a GW contribution from ocean convective sources. Figure 9b shows that during July there is a small amount of ocean thunderstorm activity, which is also seen in Figure S2 700 km east of IS17 between 6 and 12 UT. The GW ϕ in December (red) remains constant from the SE; there is some increased variability between 6 and 13 UT indicating there may be a small contribution from thunderstorms over land from the previous day, as shown in Figures 9c and S2.
In Figure 10b all months show a peak in ci between 15 and 18 UT. The peak here is likely due to the detection of GWs in very close proximity to IS17. In all three months, lightning maps show thunderstorms form overhead ITCZ, and it is likely the fast waves are detected here before they become affected by the background flow. Figure 10e shows that kH is shorter for April and December during these times, which agrees with theory. Figure 10c shows p′ in April and December peaks between 9 and 12 UT which is also when was found to be slowest in Figure 10b, agreeing with de Groot-Hedlin et al. (2017). This is also apparent in u′, in Figure 10f. The intrinsic frequency was found to have near identical minimums for all months between 10 and 14 UT; during other times there are differences between the months. This is likely due to changes to the detection performance of the infrasound array and processing algorithm, since turbulent noise is larger in the boundary layer in the middle of the day and degrades detection performance.
Figure 11 shows a histogram of detections by day which also shows a dip in the amount of GW detections being made during the middle of the day. This may distort the results for all parameters apart from ϕ as only GWs with the largest pressure amplitudes, and hence lower and larger kH, will be observed. Furthermore, by observing the lightning activity in Figures 8 and 9 there should be many GWs passing the array now due to the nearby ocean driven convection that occurs in the first half of the day. This implies there is a potential bias to slower GWs, with larger kH and p′ in the middle of the day.
In summary, ϕ is heavily modulated by the daily position of convection around IS17 which occurs over ocean in the morning and over land in the midafternoon and early evening. The intrinsic phase speed also exhibits a daily variation, while some components such as the peak at 15 to 18 UT are due to localized convection, which other parameters show agreement with. There is the potential that the diurnal variation is amplified for wave parameters due to the bias in the ability of the array to detect waves with smaller p′ during the middle of the day.
A detailed analysis of ducted GWs observed at the Ivory Coast IS17 has been undertaken, with an emphasis on establishing their source regions. This work expands on Blanc et al. (2014), by including meteorological parameters, the use of a spectral analysis to demonstrate annual and daily periodicities in , and u′, and exploring these periodicities with Met Office ATDnet lightning strike data over the region. When the ITCZ was furthest from IS17 during the summer and winter months, there is a decrease in the number of detected GWs. The GWs which were observed had smaller p′ and larger due to GW attenuation, due to the increased propagation distance between the sources, thunderstorms in the ITCZ, and the IMS station.
The spectral analysis also revealed a daily variation in all GW parameters, which was analyzed alongside lightning strike data on daily time scales for the months April, July, and December. From the lightning strike data, it was found that two convective cycles were present. The first of these, over the ocean, peaked between 03 and 12 UT, and the second, over land, peaked between 15 and 21 UT. The GW back azimuth was found to be sensitive to these different convective regions, with the back azimuth showing peak GW propagation approximately 6 hr after peak lightning activity was observed for each region. The strongest change in ϕ was during April when the ITCZ was overhead. Given the distance shown in Figure 7g, this would imply a propagation speed of ~50 m/s.
Other GW parameters were found to follow similar patterns throughout the day as the times of the convective regimes do not vary much, just their intensity. This resulted in a peak in between 15 and 18 UT when the fastest GWs generated by thunderstorms directly adjacent to the array are observed, and, during this time interval, larger wavelength waves were also detected. It is suspected that due to noise interference due to turbulence in the middle of the day, faster GWs with smaller p′ are not detected. This has a follow-on effect for the other GW parameters in that this amplifies the diurnal variation detected in the spectral analysis.
Analyses such as this provide a useful tool into understanding further how GWs are emitted from convective sources. Most modeling cases and parametrizations concentrate on the vertical propagation of GWs into the middle atmosphere (e.g., Kim et al., 2003; Beres et al., 2004; Richter et al., 2010; Lott & Guez, 2013) and seldom on trapped waves. This is because the momentum flux within the duct is near 0. However, the upper edge of the GW duct is not a perfect reflector and some GW momentum flux is released (Gill, 1982; Marlton et al., 2019; Nappo, 2013) potentially releasing momentum flux far from the convective source. Studies such as de Groot-Hedlin et al. (2017) have shown agreement between stratospheric measurements of GWs and ground-based measurements, allowing a global infrasound network such as the IMS to provide a proxy for stratospheric GW measurements.
This work was performed during the course of the ARISE2 collaborative infrastructure design study project funded by the European Commission H2020 program (grant number 653980, arise-project.eu). The authors would like to acknowledge Station Géophysique de Lamto in Ivory Coast for their work in maintaining the IS17 infrasound station and the French Atomic Energy Commission (CEA) for the processing and provision of the infrasound and meteorological data from IS17. The gravity wave climatology is available to download from the University of Reading's data repository at http://dx.doi.org/10.17864/1947.199 to be added when available. The UK Met Office ATDnet data were provided by Sven-Eric Enno and are available on request. Model data from the ECMWF are available through the ECMWF's MARS archive.
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